> Over any specified time period, the market return will be a weighted average of the returns on the securities within the market, using beginning market values as weights[3]. Each passive manager will obtain precisely the market return, before costs[4]. From this, it follows (as the night from the day) that the return on the average actively managed dollar must equal the market return. Why? Because the market return must equal a weighted average of the returns on the passive and active segments of the market. If the first two returns are the same, the third must be also.
> This proves assertion number 1. Note that only simple principles of arithmetic were used in the process. To be sure, we have seriously belabored the obvious, but the ubiquity of statements such as those quoted earlier suggests that such labor is not in vain.
> To prove assertion number 2, we need only rely on the fact that the costs of actively managing a given number of dollars will exceed those of passive management. Active managers must pay for more research and must pay more for trading. Security analysis (e.g. the graduates of prestigious business schools) must eat, and so must brokers, traders, specialists and other market-makers.
> Because active and passive returns are equal before cost, and because active managers bear greater costs, it follows that the after-cost return from active management must be lower than that from passive management.
* https://web.stanford.edu/~wfsharpe/art/active/active.htm
And on why picking a winning stock is so hard (first edition 1973):
* https://en.wikipedia.org/wiki/A_Random_Walk_Down_Wall_Street